Substrate Logistics: A Synthesis of the Universal Attenuation Tensor ($\mathcal{T}_\Omega$) from First Principles
Year: 2026
Type: article
Abstract: Title: Substrate Logistics: A Synthesis of the Universal Attenuation Tensor ($\mathcal{T}_\Omega$) from First Principles Author: Marco Lindenbeck Description: Standard Quantum Field Theory and General Relativity treat the $10^{19}$ magnitude gap between the hadronic scale and the Planck scale as an empirical fine-tuning anomaly, commonly known as the Hierarchy Problem. This manuscript provides a concise synthesis of the Substrate Logistics framework, illustrating how the Universal Attenuation Tensor ($\mathcal{T}_\Omega \approx 1.30147 \times 10^{19}$) emerges naturally as a parameter-free geometric constant of nature. By modeling the vacuum substrate as a Poincaré Dodecahedral Space ($S^3/\mathcal{I}^*$), this paper traces the deterministic pipeline from the binary icosahedral group to the Topological Resolution Constant ($\kappa=50$), the Universal Topological Drag ($\mathcal{C}_\delta \approx 4.7214 \times 10^{-4}$), the Bare-Metal Buffer Scalar ($\mathcal{B}_{max}=400/3$), and the 10D Metric Tensor Expansion ($\mathcal{A}_\Omega=50^{10}$). We demonstrate that the $10^{19}$ Planck expansion and $10^{38}$ gravitational attenuation are direct, un-tuned consequences of discrete metric geometry, resolving the Hierarchy Problem without empirical fine-tuning or speculative extra spatial dimensions.
Author: Lindenbeck, Marco
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212439206
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